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Archivio digitale delle tesi discusse presso l’Università di Pisa

Tesi etd-05222023-163719


Tipo di tesi
Tesi di laurea magistrale
Autore
PAPALLO, FILIPPO
URN
etd-05222023-163719
Titolo
Braid group actions on derived categories
Dipartimento
MATEMATICA
Corso di studi
MATEMATICA
Relatori
relatore Prof. Talpo, Mattia
Parole chiave
  • action
  • algebraic geometry
  • braid groups
  • category
  • derived categories
  • DG-algebra
  • homological algebra
  • mapping class group
  • topology
Data inizio appello
09/06/2023
Consultabilità
Completa
Riassunto
The aim of this thesis is to explain the construction of the ``spherical twists'' invented by P. Seidel and R. Thomas. After defining ``spherical objects'' in the bounded derived category of a fairly general $k$-linear category, we will define the ``spherical twist'' associated to it and study its main property: in particular, this produces an exact autoequivalence of the derived category. If a sequence of spherical objects satisfies some ``adjacency condition'', then their spherical twist satisfy the braid relations, thus one can define an action of some braid group $\Br_{m+1}$ on such derived categories. It is a non-trivial fact that this action is faithful: in order to work out the proof, a consistent amount of techniques from differential graded algebra are discussed.
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